MMSE iterative equalization method of OTSM system in high-speed mobile environment

Abstract

The invention belongs to the technical field of communication, and particularly relates to an MMSE iterative equalization method of an OTSM system in a high-speed mobile environment. The method comprises the following steps: constructing an OTSM system model, wherein the OTSM system model comprises a sending end, a time domain channel and a receiving end; processing the data output by the time domain channel by using a block time frequency single-tap equalizer to obtain a time delay-time domain information symbol estimated value; the time delay-time domain information symbol pre-estimated value is judged to serve as initial estimation of a GS algorithm for iterative detection; calculating a mean value and a variance according to time delay-time domain information symbol estimation values obtained by multiple iterations; performing iterative detection by taking the mean value and the variance as initial estimations of an MP algorithm, and outputting a judgment of a transmission symbol from a sending end to a receiving end through a time domain channel; according to the method, the residual symbol interference can be effectively eliminated, so that the reliability and the transmission quality of the system are greatly improved.

Description

Technical Field

[0001] The invention belongs to the field of communication technology, and in particular relates to an MMSE iterative equalization method for an OTSM system in a high-speed mobile environment. Background Art

[0002] The sixth generation (6G) wireless network is expected to provide reliable communications for high carrier frequency and high mobility scenarios, such as drones, low earth orbit satellites, and high-speed trains. Although traditional orthogonal frequency division multiplexing (OFDM) can effectively reduce signal distortion and interference and has high spectrum efficiency. However, due to the high frequency dispersion caused by Doppler shift, the performance of systems based on orthogonal frequency division multiplexing (OFDM) is severely degraded in high mobility communication scenarios. In order to combat the dispersion effect of the channel, especially the high Doppler effect, orthogonal time frequency space modulation (OTFS) modulation was proposed. The main idea of ​​OTFS modulation is to place the information symbols in the delay-Doppler (DD) domain, which results in a 2D convolution of the information symbols with the channel in the DD domain. Studies have found that in high Doppler communication scenarios, the performance of OTFS is better than OFDM.

[0003] like Figure 1 As shown in the figure, the OTSM system cleverly combines the characteristics of time delay and Doppler spread, allowing the channel to introduce inter-symbol interference (ISI inter-symbol interference) in different dimensions of time delay and sequence, and finally performing separation operations at the receiving end. This technology can effectively suppress large-scale coherent speckle noise and phase delay distortion caused by the Doppler effect in narrowband or broadband radar echoes, while also achieving better spectral purity and resolution. In this way, the rapidly changing time-frequency domain channel is converted into an approximately constant non-fading channel, which facilitates signal transmission and processing. Compared with OTFS, which performs IFFT in the Doppler domain, OTSM has a lower complexity. This is because the WHT transform does not involve other complex multiplications, but only addition and subtraction operations, which is more efficient and simple.

[0004] In terms of two-dimensional detection algorithms, there is an iterative detection algorithm based on message passing (MP), which takes advantage of the sparsity of DD domain channels and iterative processing, can eliminate interference and improve detection performance. In addition, there is a low-complexity iterative detector, which is designed based on the system characteristics of OTSM, similar to a two-stage equalizer, and aims to solve the interference problem in the OTSM system. In order to cope with the challenges brought by wireless channels with high Doppler frequency shift, this scheme adopts an improved design. First, a single-tap minimum mean square error (MMSE) equalizer is introduced in the TF domain. The design of this equalizer aims to suppress the interference between carriers and reduce the impact of Doppler frequency shift on the signal. Next, an improved iterative detection algorithm, namely the Gauss-Seidel (GS) iterative detection algorithm, is adopted in the time domain. This algorithm further eliminates residual symbol interference through multiple iterations. Compared with the traditional GS algorithm, this improved scheme can better adapt to the situation of high Doppler frequency shift. However, although this design has made some improvements, there are still some problems when facing wireless channels with high Doppler shift. Specifically, the rapid change and frequency expansion of the channel make channel estimation difficult, affecting the performance of the equalizer and GS algorithm. Although the improved GS algorithm can better adapt to high Doppler shift, the algorithm still needs to be further optimized to improve its convergence and error performance when facing rapidly changing wireless channels. The current design is limited in this case, resulting in serious impact on the convergence speed and error performance of the GS iterative detection algorithm.

[0005] In summary, it is necessary to further improve the design of the secondary equalizer in view of the particularity of high Doppler frequency shift wireless channels. Solving this problem is crucial to further optimize the performance of the OTSM system and improve the reliability of data transmission. Summary of the invention

[0006] In view of the shortcomings of the prior art, the present invention proposes an MMSE iterative equalization method for an OTSM system in a high-speed mobile environment, the method comprising:

[0007] S1: construct an OTSM system model, wherein the OTSM system model includes a transmitter, a time domain channel and a receiver;

[0008] S2: Use a block time-frequency single-tap equalizer to process the data output by the time domain channel to obtain a delay-time domain information symbol estimate;

[0009] S3: The estimated value of the delay-time domain information symbol is used as the initial estimate of the GS algorithm for iterative detection after judgment; the mean and variance of the delay-time domain information symbol obtained by multiple iterations are calculated;

[0010] S4: Use the mean and variance as initial estimates of the MP algorithm for iterative detection, and output the decision of the transmission symbol from the transmitter to the receiver through the time domain channel.

[0011] Preferably, the process of processing the data output by the time domain channel using a block time-frequency single-tap equalizer includes:

[0012] The time domain vector output by the time domain channel is divided into N time domain blocks, and M-point FFT is performed on each of them to obtain N frequency domain blocks;

[0013] Perform MMSE equalization on each frequency domain block to obtain information symbols of multiple frequency domain blocks;

[0014] Perform M-point IFFT on the information symbol of each frequency domain block to obtain a delay-time domain information symbol estimate.

[0015] Preferably, in step S3, the process of iterative detection using the GS algorithm includes:

[0016] S31: After the symbol vector of each time domain block is determined, a time domain information symbol is obtained; the time domain information symbol is subjected to matched filtering operation to obtain a time domain input-output relationship;

[0017] S32: using the GS method to iteratively solve the least square solution corresponding to the time domain input-output relationship, and obtain the delay-time domain information symbol estimation value of the current iteration;

[0018] S33: performing hard decision on the iterative least square solution to obtain a delayed sequence domain information symbol in each iteration process;

[0019] S34: The delayed sequence domain information symbol is relaxed and scaled to obtain a new delay-time domain information symbol and use it as the initial value in the next iteration process, and steps S32 to S34 are repeated until a preset number of iterations is reached.

[0020] Preferably, in step S4, the process of iteratively detecting the mean and variance as initial estimates of the MP algorithm includes:

[0021] S41: Initialize probability mass function;

[0022] S42: The observation node passes the mean and variance to the variable node;

[0023] S43: the variable node updates the probability mass function using the current probability mass function, mean and variance, and passes the new probability mass function to the observation node;

[0024] S44: Calculate the convergence indicator and update the mean and variance;

[0025] S45: if the current convergence indicator is greater than the convergence indicator of the previous iteration, updating the transmission symbol according to the current probability mass function;

[0026] S46: Determine whether the convergence indicator satisfies the stopping criterion. If the convergence indicator satisfies the stopping criterion or the number of iterations reaches the maximum number of iterations, output the transmission symbol; otherwise, return to step S42.

[0027] Furthermore, the formula for updating the probability mass function is:

[0028]

[0029] in, Represents the symbol a passed from variable node c to observation node d in the i-th iteration j The posterior probability of α represents the damping factor, a j represents the jth symbol, Represents the symbol a passed from variable node c to observation node d in the i-th iteration j The estimated value of Represents the symbol a passed from variable node c to observation node d in the i-1th iteration j The posterior probability of .

[0030] Furthermore, the formula for calculating the convergence indicator is:

[0031]

[0032] Among them, η (i) represents the convergence indicator of the i-th iteration, N represents the number of symbols in the system, M represents the number of subcarriers in the system, and a j represents the jth symbol, Indicates the symbol a in the i-th iteration j The probability value at position c, γ represents the threshold, represents a symbol set, and I(·) represents an indicator function.

[0033] Furthermore, the formulas for updating the mean and variance are:

[0034]

[0035] in, Indicates the symbol a in the i-th iteration j The statistical mean of the estimated values, Represents the symbol a transmitted from any intermediate node e to the observation node d in the i-1th iteration j The posterior probability ofj represents the jth symbol, H[d,e] represents the channel matrix, Q represents the constant for normalizing all possible symbols, I(d) represents the indicator function, Indicates the symbol a in the i-th iteration j Statistical variance of the estimate, σ 2 represents the noise variance.

[0036] Furthermore, the formula for updating the transmission symbol is:

[0037]

[0038] in, represents the estimated value of the symbol at the cth position, Indicates the symbol a in the i-th iteration j The probability value at position c, a j represents the jth symbol, Represents a symbol set.

[0039] Furthermore, the stopping criterion is that the convergence indicator is 1 or the condition is satisfied:

[0040] η (i) <η (i*) -ε

[0041] Among them, η (i) represents the convergence indicator of the i-th iteration, η (i*) represents the maximum convergence indicator and ε represents a small constant.

[0042] The beneficial effects of the present invention are as follows: considering the high Doppler frequency shift brought by high-speed mobile environment and the inter-symbol interference caused by multipath transmission, the present invention first uses block-by-block MMSE detection in the time-frequency domain to accurately recover and demodulate the signal, suppress the interference between carriers and reduce the impact of Doppler frequency shift on the signal, and then uses the Gauss-Seidel (GS) method of matched filtering for a certain number of iterations as the initial estimate, and then captures the direct and indirect dependencies between variables through Bayesian networks and Malchev random fields at the observation node and the variable node, and updates information to perform iterative detection. The computational efficiency of the GS iterative method is used to effectively reduce the number of iterations of message passing (MP), and at the same time provide a better initial estimate, thereby reducing the overall computational complexity and improving the bit error performance. The system of the present invention can effectively eliminate residual symbol interference, thereby greatly improving the reliability and transmission quality of the system. According to the simulation results, compared with the traditional GS iterative detection method based on single-tap equalization and the MP iterative detection method based on single-tap equalization, the algorithm proposed by the present invention achieves a significant improvement in bit error performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 The relationship between different discrete signal symbol domains and corresponding modulation schemes;

[0044] Figure 2 It is a flow chart of the MMSE iterative equalization method in the present invention;

[0045] Figure 3 This is a diagram of the OTSM system transceiver model in the present invention;

[0046] Figure 4 It is the information graph of observation node and variable node factor graph in the present invention;

[0047] Figure 5 It is a bit error performance diagram under different equalization algorithms in the OTSM system of the present invention;

[0048] Figure 6 The bit error performance of the OTSM system in the present invention under different detection algorithms;

[0049] Figure 7 The error performance of the present invention and the comparison algorithm is compared at different speeds and signal-to-noise ratios. DETAILED DESCRIPTION

[0050] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0051] The present invention proposes an MMSE iterative equalization method for an OTSM system in a high-speed mobile environment. Figure 2 As shown, the method includes the following contents:

[0052] S1: construct an OTSM system model, wherein the OTSM system model includes a transmitting end, a time domain channel and a receiving end.

[0053] Construct the OTSM system model and use the following matrix / vector to represent the OTSM system. For the transmission of OTSM signal frames, the total frame duration is set to T f =NT, the bandwidth is B=MΔf, where Δf=1 / T, the signal is sampled strictly according to the pulse shaping waveform, and N is selected as a power of 2. Figure 3 The transmission model of the OTSM system is shown.

[0054] At the sending end, the information symbol is divided into m symbol vectors Each symbolic vector x m are placed in the mth row of the matrix, and all symbol vectors are neatly arranged into the matrix The column index and the row index are used to represent the delay index and the sequence index of the delay sequence grid, respectively.

[0055] X=[x0,x1,…,x M-1 ] T (1)

[0056] Then add X to the last l max The rows are set to zero vectors, where l max represents the discrete channel delay spread index. Figure 3 As shown, zero padding (ZP) along the delay domain helps to avoid inter-block interference due to channel delay spread. For each symbol vector x m Perform an N-point WHT transformation and convert it to the delay time domain:

[0057]

[0058] matrix Contains the delayed time samples, which are vectorized to obtain the delayed time domain symbol vector It is finally sent to the channel, where each symbol vector represents a signal sample at a specific time delay.

[0059]

[0060] At the receiving end, after analog-to-digital conversion and sampling, the time domain signal r(t) is demodulated in the reverse order of the transmitting end to obtain the received time domain vector. is the time domain vector after RF front-end operation and ADC sampling. The received information symbol y is arranged in columns into a matrix Each column corresponds to a received symbol vector.

[0061]

[0062] right Perform N-point WHT changes to obtain information symbol Y in the DS domain, where:

[0063]

[0064] In the time domain channel part, the baseband equivalent channel model includes P propagation paths, each with a different gain v i , delay offset τ i and Doppler frequency shift v i . Assume that the maximum delay spread of the channel is τ max , the maximum Doppler spread is v maxThe corresponding Doppler spread length and channel delay spread length are α = [v max NT] and β = [τ max MΔf]. In an OTSM system with a carrier frequency of 4 GHz and a subcarrier spacing of 15 kHz, the extended vehicular channel model (EVA) is assumed. In this setting, the delay-Doppler spread length is α=10, β=3, which is significantly smaller than the number of sampling points NM of the system.

[0065] Since the number of propagation paths P in the delay-Doppler domain channel is usually limited, the delay-Doppler domain channel response can be expressed as:

[0066]

[0067] The corresponding continuous time-varying channel impulse response function can be expressed as

[0068] g(τ,v)=∫ v h(τ,v)e jπ2v(t-τ) dv (7)

[0069] Starting from the received time domain signal r(t), the continuous time domain input-output relationship can be expressed as

[0070]

[0071] Therefore, the input-output relationship in the time domain can be expressed as

[0072] r=H·s+w (9)

[0073] in, The mean is 0 and the variance is Gaussian white noise, is the discrete channel matrix in the time domain.

[0074]

[0075] in,

[0076] Due to the introduction of zero padding (ZP) in the time domain, inter-block interference in the time domain is effectively avoided. Therefore, in the time domain, the input-output relationship in equation (9) is separated and can be processed independently, which can be expressed as

[0077] r n =H n ·s n +w n ,n=0,...,N-1 (11)

[0078] in, And H nis the nth time-domain block channel matrix.

[0079] It is noteworthy that due to the Walsh-Hadamard expansion, all N time-domain blocks have equal components with each delayed sequence-domain information symbol.

[0080] S2: Use a block time-frequency single-tap equalizer to process the data output by the time domain channel to obtain a delay-time domain information symbol estimate.

[0081] In the case of a static (or very low Doppler spread) wireless channel, the time domain channel matrix of each block is assumed to be a circulant matrix, so it can be diagonalized in the frequency domain. For a given subcarrier and reference signal sequence, each frame can be transmitted using multiple channels, and each subblock consists of the corresponding channels. However, in mobile channels, due to the presence of time-varying channels, Doppler spread will cause interference between the frequency domain samples of each block, resulting in the time domain channel matrix no longer being cyclic. A frame will have good performance if it contains multiple subcarriers and the cross-correlation function value between two adjacent subcarriers is greater than a given threshold. However, considering that the duration of each time domain block is short relative to the entire frame, it can be assumed that the channel in each block is constant, but there are differences between each block. The advantage of this is that it allows the use of a single-tap MMSE equalizer to detect in each block and then use WHT to combine the block estimates.

[0082] Perform M-point FFT operation on the received time domain block to obtain the time-frequency block corresponding to the time domain block

[0083]

[0084] Then, each time-frequency block can be subjected to MMSE equalization to obtain the information symbol of the frequency domain block:

[0085]

[0086] Where m=0,...,M-1, n=0,...,N-1, For the AWGN noise variance of each time domain block, the frequency domain channel coefficient can be expressed by the following formula:

[0087]

[0088] Among them, F M Represents the transformation matrix for FFT operation on time domain signal, Represents the conjugate transpose of the transform matrix for performing FFT operations on time domain signals.

[0089] An M-point IFFT operation is performed on the information symbol of the frequency domain block to obtain a delay-time domain information symbol estimation value.

[0090]

[0091] S3: The estimated value of the delay-time domain information symbol is used as the initial estimate of the GS algorithm for iterative detection after judgment; the mean and variance of the delay-time domain information symbols obtained through multiple iterations are calculated.

[0092] Dividing the entire frame into short blocks can assume that the channel remains constant within the duration TTT of each block. However, in the case of high Doppler spread, this assumption may lead to performance degradation, especially for high-order QAM symbols.

[0093] The present invention adopts a matched filtered Gauss-Seidel message passing algorithm (MF-GMP, Matched FilteredGauss-Seidel Message Passing) to achieve equalization. First, a Gauss-Seidel (GS) method is used to perform iterative estimation for a certain number of times, and then the estimated mean and variance are returned as soft information of the MP algorithm and used as an initial estimation. Then, the probability mass function and the mean and variance are calculated through observation nodes and variable nodes, and information is updated mutually for iterative detection.

[0094] First, the GS algorithm is used for iterative detection; the mean and variance are calculated based on the delay-time domain information symbols obtained through multiple iterations; specifically:

[0095] S31: After the symbol vector of each time domain block is determined, a time domain information symbol is obtained; the time domain information symbol is subjected to matched filtering operation to obtain a time domain input-output relationship.

[0096] GS iterations are performed on matched filter channel matrix blocks The matrix input-output relationship after the time domain information symbol matching filter operation in (9) can be written as:

[0097]

[0098] in, and

[0099] S32: Use the GS method to iteratively solve the least square solution corresponding to the time domain input-output relationship to obtain the delay-time domain information symbol of the current iteration.

[0100] Use the GS method to iteratively find the least squares solution of the M-dimensional linear equation system in (16)

[0101]

[0102] Let D n and L n is the matched filter matrix Rn The matrix of diagonal elements and lower triangular elements of . In each iteration, find s n The GS iterative method for the estimate is given by:

[0103]

[0104] Where T n ∈C M×M is the GS iteration matrix, the vector The estimated value of the transmitted time domain samples of the nth block in the i-th iteration is the delay-time domain information symbol estimate.

[0105] S33: Perform hard decision on the iterative least square solution to obtain delayed sequence domain information symbols in each iteration process.

[0106] The delayed sequence domain information in the i-th iteration is expressed as:

[0107]

[0108] in And D(.) denotes the decision function, which replaces all elements of the input with the nearest QAM symbol (measured in terms of Euclidean distance).

[0109] S34: The delayed sequence domain information symbol is relaxed and scaled to obtain a new delay-time domain information symbol and use it as the initial value in the next iteration process, and steps S32 to S34 are repeated until a preset number of iterations is reached.

[0110] The hard decision estimate is transformed back to the time domain to update the time domain estimate to be used in the next iteration:

[0111]

[0112] Here, δ is a relaxation parameter used to improve the detector convergence for higher modulation schemes such as 64-QAM.

[0113] The present invention needs to balance the number of GS iterations. Too many GS iterations may linger around the local optimum, and too few GS iterations may not provide a sufficiently good initial value. Preferably, the present invention uses Monte Carlo simulation to calculate the optimal number of iterations.

[0114] S4: Use the mean and variance as initial estimates of the MP algorithm for iterative detection, and output the decision of the transmission symbol from the transmitter to the receiver through the time domain channel.

[0115] Figure 4The connection and message passing between the observation node and the variable node are shown, where the circles represent the variable nodes and the squares represent the observation nodes. In the MP algorithm, the mean and variance of the interference term are used as the information sent from the observation node y[d] to the variable node x[c] to achieve information transmission. On the other hand, from the symbol node x[c] to y[d], the corresponding probability mass function (pmf) is transmitted, where d∈J(c).

[0116] S41: Initialize the probability mass function.

[0117]

[0118] S42: The observation node passes the mean and variance to the variable node.

[0119] The present invention uses the estimated mean and estimated variance previously iterated by MMSE and GS to replace the estimated mean and variance of the original MP iterative algorithm.

[0120] S43: The variable node updates the probability mass function using the current probability mass function, mean and variance, and passes the new probability mass function to the observation node.

[0121] (pmf) vector Can be updated to:

[0122]

[0123] in, Indicates the symbol a in the i-th iteration j The probability value of Indicates the symbol a in the i-th iteration j The estimated value of Represents the symbol a passed from variable node c to observation node d in the i-1th iteration j The posterior probability of , Δ∈(0,1] is the damping factor used to improve the performance by controlling the convergence speed, and:

[0124]

[0125] in,

[0126] S44: Calculate the convergence indicator and update the mean and variance.

[0127] The formula for calculating the convergence indicator is:

[0128]

[0129] Among them, η (i)represents the convergence indicator of the i-th iteration, N represents the number of symbols in the system, M represents the number of subcarriers in the system, Indicates the symbol a in the i-th iteration j The probability value at position c, γ>0 represents the threshold, Represents the symbol set, which contains all possible symbols; I(·) represents the indicator function, which is specific if the independent variable If there is a true expression in the memory, the specific value of this indicator function will be 1, otherwise, the result will be 0.

[0130] The formulas for updating the mean and variance are:

[0131]

[0132] in, Indicates the symbol a in the i-th iteration j The statistical mean of the estimated values, Represents the symbol a transmitted from any intermediate node e to the observation node d in the i-1th iteration j The posterior probability of j represents the jth symbol, H[d,e] represents the channel matrix, Q represents the constant for normalizing all possible symbols, I(d) represents the indicator function, Indicates the symbol a in the i-th iteration j Statistical variance of the estimate, σ 2 represents the noise variance.

[0133] S45: If the current convergence indicator is greater than the convergence indicator of the previous iteration, the transmission symbol is updated according to the current probability mass function.

[0134] If η (i) >η (i-1) , then update the transmission symbol:

[0135]

[0136] in, represents the estimated value of the symbol at the cth position, Indicates the symbol a in the i-th iteration j The probability value at position c is, Represents the symbol set, containing all possible symbols.

[0137] The algorithm updates its decision regarding transmitted symbols only if the current iteration gives us a better estimate than the last one.

[0138] S46: Determine whether the convergence indicator satisfies the stopping criterion. If the convergence indicator satisfies the stopping criterion or the number of iterations reaches the maximum number of iterations, output the transmission symbol; otherwise, return to step S42.

[0139] The algorithm stops when at least one of the following conditions is met.

[0140] 1)η (i) =1.

[0141] 2)η (i) <η (i*) -ε, where i* is the iteration index from {1,…,(i-1)}, where η (i*) maximum.

[0142] 3) The maximum number of iterations is reached. Preferably, ε=0.2 is selected to ignore small fluctuations in η.

[0143] After the MP algorithm is iterated and detected, the output of the transmission symbol from the transmitter to the receiver through the time domain channel is the instant delay-time domain information symbol estimation value.

[0144] Walsh-Hadamard transform is performed on the estimated value of the delay-time domain information symbol to obtain the estimated value of the delay-sequence domain information symbol.

[0145] Evaluation of the present invention:

[0146] The present invention uses block MMSE for initial estimation to suppress interference between carriers and reduce the impact of Doppler frequency shift on the signal, and uses the GS algorithm to perform a certain number of iterations as the initial value to assign to the MP algorithm for initial estimation, thereby improving the bit error performance. At the same time, the computational efficiency of the GS can be used to effectively reduce the number of iterations of the MP algorithm, thereby reducing the overall computational complexity. The availability of low-complexity detection methods makes OTSM an attractive candidate for future wireless communication networks.

[0147] The block MMSE Gauss-Seidel iterative equalization algorithm based on message passing and the existing iterative detection algorithm are simulated and compared, and the simulation parameters in Table 1 are used without special explanation. As shown in Table 1, in the following simulation, OTSM frames with N = 32 and M = 32 are generated. The subcarrier spacing Δf is 15kHz and the carrier frequency is 4GHz. The maximum delay spread (in terms of integer taps) is set to 4 (l max =4), which is about 4 μs, so the maximum number of delay taps seen by the discrete receiver is L = 4. The channel delay model is generated based on the standard EVA model in

[23] . Each point in the BER graph sends 10 5 Frame signal, channel Doppler shift is calculated by Jakes formula v i =vmax cos(θ i ) generated, v max is the maximum moving speed and θ i Uniformly distributed on [-π,π].

[0148] Table 1 Simulation parameters

[0149]

[0150] according to Figure 5 From the displayed results, we can see that under high signal-to-noise ratio conditions and different equalization algorithms, the proposed algorithm has a significant improvement in error performance compared to the traditional GS and MP algorithms. At the same time, the iterative detection algorithm based on the block frequency domain single-tap equalizer has a significant improvement in error performance compared to the single-tap equalizer iterative detection algorithm. This is mainly because the proposed algorithm has a significant improvement in error performance compared to the traditional GS and MP algorithms by improving initial estimation, effectively handling complex interference factors, reducing complexity and number of iterations, and designing a better equalizer. Under high signal-to-noise ratio conditions, these improvements can give full play to the advantages of the algorithm and improve the overall performance of the system. This means that in a high signal-to-noise ratio environment, the proposed algorithm can more effectively equalize and detect signals, thereby achieving better error performance. In comparison, the traditional single-tap frequency domain equalization combined with the GS iterative algorithm and the time domain block equalization combined with the GS iterative algorithm, as well as the single-tap frequency domain equalization combined with the MP iterative algorithm and the time domain block equalization combined with the MP iterative algorithm may perform poorly in this case. Comprehensive Figure 5 The results show that the proposed algorithm can achieve better performance under high signal-to-noise ratio conditions, which shows that the algorithm has a good performance advantage in the OTSM system.

[0151] according to Figure 6 From the comparison results, we can see that under high signal-to-noise ratio conditions and different modulation modes, the proposed algorithm is still applicable to different modulation modes, and the iterative detection algorithm based on the block frequency domain single-tap equalizer still has a significant improvement in error performance compared to the iterative detection algorithm based on the single-tap equalizer. Figure 6 The results show that the proposed algorithm can achieve better performance under different modulation modes and high signal-to-noise ratio conditions, which shows that the algorithm has good applicability in the OTSM system.

[0152] In order to more intuitively evaluate the performance of the GS algorithm, MP algorithm and the proposed algorithm under different user mobility rates and signal-to-noise ratios, we conducted a three-dimensional in-depth analysis of the GS algorithm, MP algorithm and the proposed algorithm. Figure 7 As shown in Figure 1, Figure (a) shows the three-dimensional view of user speed, signal-to-noise ratio and algorithm, and Figures (b), (c) and (d) show the three-dimensional views at different angles for clearer observation. Figure 7It can be seen that with the increase of speed and signal-to-noise ratio, the proposed algorithm has a better performance advantage than the traditional GS and MP algorithms. Therefore, the proposed algorithm can well meet the requirements of future wireless mobile communication systems.

[0153] In summary, the present invention first uses block-by-block MMSE detection in the time-frequency domain to accurately recover and demodulate the signal, suppress the interference between carriers and reduce the impact of Doppler frequency shift on the signal, and then uses the Gauss-Seidel (GS) method of matched filtering for a certain number of iterations as the initial estimate, and then captures the direct and indirect dependencies between variables through Bayesian networks and Malchev random fields at the observation node and the variable node, and updates information with each other for iterative detection. The computational efficiency of the GS iterative method is used to effectively reduce the number of iterations of message passing (MP), and at the same time provide a better initial estimate, thereby reducing the overall computational complexity and improving the bit error performance. Simulation experiments show that the bit error performance of the equalizer is significantly improved under different speeds, systems and modulation modes, especially in high-speed mobile environments. This innovative research is of great significance to improving the performance of the OTSM system, and provides a more reliable and high-quality signal processing solution for wireless communication systems in practical applications. The excellent performance of the algorithm proposed in the present invention under high-speed mobile conditions is of great significance for applications in fields such as mobile communications and Internet of Vehicles, and lays a solid foundation for providing high-quality communication services.

[0154] The above embodiments further illustrate the purpose, technical solutions and advantages of the present invention in detail. It should be understood that the above embodiments are only preferred implementation modes of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made to the present invention within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. An MMSE iterative equalization method for an OTSM system in a high-speed mobile environment, characterized in that: The following steps are involved: S1: construct an OTSM system model, wherein the OTSM system model includes a transmitter, a time domain channel and a receiver; S2: Use a block time-frequency single-tap equalizer to process the data output by the time domain channel to obtain a delay-time domain information symbol estimate; S3: The estimated value of the delay-time domain information symbol is used as the initial estimate of the GS algorithm for iterative detection after judgment; the mean and variance are calculated based on the estimated value of the delay-time domain information symbol obtained through multiple iterations; S4: Use the mean and variance as initial estimates of the MP algorithm for iterative detection, and output the decision of the transmission symbol from the transmitter to the receiver through the time domain channel.

2. The MMSE iterative equalization method of an OTSM system in a high-speed mobile environment according to claim 1, characterized in that: The process of processing the data output by the time domain channel using the block time-frequency single-tap equalizer includes: The time domain vector output by the time domain channel is divided into N time domain blocks, and M-point FFT is performed on each of them to obtain N frequency domain blocks; Perform MMSE equalization on each frequency domain block to obtain information symbols of multiple frequency domain blocks; Perform M-point IFFT on the information symbol of each frequency domain block to obtain a delay-time domain information symbol estimate.

3. The MMSE iterative equalization method of an OTSM system in a high-speed mobile environment according to claim 1, characterized in that: In step S3, the process of iterative detection using the GS algorithm includes: S31: After the symbol vector of each time domain block is determined, a time domain information symbol is obtained; the time domain information symbol is subjected to matched filtering operation to obtain a time domain input-output relationship; S32: using the GS method to iteratively solve the least square solution corresponding to the time domain input-output relationship, and obtain the delay-time domain information symbol estimation value of the current iteration; S33: performing hard decision on the iterative least square solution to obtain a delayed sequence domain information symbol in each iteration process; S34: The delayed sequence domain information symbol is relaxed and scaled to obtain a new delay-time domain information symbol and use it as the initial value in the next iteration process, and steps S32 to S34 are repeated until a preset number of iterations is reached.

4. The MMSE iterative equalization method of an OTSM system in a high-speed mobile environment according to claim 1, characterized in that: In step S4, the process of iteratively detecting the mean and variance as initial estimates of the MP algorithm includes: S41: Initialize probability mass function; S42: The observation node passes the mean and variance to the variable node; S43: the variable node updates the probability mass function using the current probability mass function, mean and variance, and passes the new probability mass function to the observation node; S44: Calculate the convergence indicator and update the mean and variance; S45: if the current convergence indicator is greater than the convergence indicator of the previous iteration, updating the transmission symbol according to the current probability mass function; S46: Determine whether the convergence indicator satisfies the stopping criterion. If the convergence indicator satisfies the stopping criterion or the number of iterations reaches the maximum number of iterations, output the transmission symbol; otherwise, return to step S42.

5. The MMSE iterative equalization method of an OTSM system in a high-speed mobile environment according to claim 4, characterized in that: The formula for updating the probability mass function is: in, Represents the symbol a passed from variable node c to observation node d in the i-th iteration j The posterior probability of j represents the jth symbol, Represents the symbol a passed from variable node c to observation node d in the i-th iteration j The estimated value of Represents the symbol a passed from variable node c to observation node d in the i-1th iteration j The posterior probability of .

6. The MMSE iterative equalization method of an OTSM system in a high-speed mobile environment according to claim 4, characterized in that: The formula for calculating the convergence indicator is: Among them, η (i) represents the convergence indicator of the i-th iteration, N represents the number of symbols in the system, M represents the number of subcarriers in the system, and a j represents the jth symbol, Indicates the symbol a in the i-th iteration j The probability value at position c, γ represents the threshold, represents a symbol set, and I(·) represents an indicator function.

7. The MMSE iterative equalization method for an OTSM system in a high-speed mobile environment according to claim 4, characterized in that: The formulas for updating the mean and variance are: in, Indicates the symbol a in the i-th iteration j The statistical mean of the estimated values, Represents the symbol a transmitted from any intermediate node e to the observation node d in the i-1th iteration j The posterior probability of j represents the jth symbol, H[d,e] represents the channel matrix, Q represents the constant for normalizing all possible symbols, I(d) represents the indicator function, Indicates the symbol a in the i-th iteration j Statistical variance of the estimate, σ 2 represents the noise variance.

8. The MMSE iterative equalization method for an OTSM system in a high-speed mobile environment according to claim 4, characterized in that: The formula for updating the transmission symbol is: in, represents the estimated value of the symbol at the cth position, Indicates the symbol a in the i-th iteration j The probability value at position c, a j represents the jth symbol, Represents a symbol set.

9. The MMSE iterative equalization method of an OTSM system in a high-speed mobile environment according to claim 4, characterized in that: The stopping criteria are the convergence indicator being 1 or satisfying the condition: or (i) <the> (i*) -e Among them, η (i) represents the convergence indicator of the i-th iteration, η (i*) represents the maximum convergence indicator and ε represents a small constant.

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